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The maximum Wiener index of some oriented graphs

Author

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  • Meng, Xianhao
  • Zhang, Yuwan
  • Zhao, Weichen

Abstract

The Wiener index W(D) of a digraph D is defined as the sum of distances between all ordered pairs of vertices. In directed graphs, a specific convention is adopted: when there exists no directed path connecting vertex a to vertex b, the distance d(a, b) is defined as 0. Notably, this particular stipulation has been put forward independently in a number of research works focusing on directed graphs. In this paper, we obtain the maximum Wiener index of the oriented fan graphs and wheel graphs.

Suggested Citation

  • Meng, Xianhao & Zhang, Yuwan & Zhao, Weichen, 2026. "The maximum Wiener index of some oriented graphs," Applied Mathematics and Computation, Elsevier, vol. 514(C).
    • Handle: RePEc:eee:apmaco:v:514:y:2026:i:c:s0096300325005612
    DOI: 10.1016/j.amc.2025.129836
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    References listed on IDEAS

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    1. Knor, Martin & Škrekovski, Riste & Tepeh, Aleksandra, 2016. "Some remarks on Wiener index of oriented graphs," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 631-636.
    2. Knor, Martin & Škrekovski, Riste & Tepeh, Aleksandra, 2016. "Digraphs with large maximum Wiener index," Applied Mathematics and Computation, Elsevier, vol. 284(C), pages 260-267.
    3. Debarun Ghosh & Ervin Győri & Addisu Paulos & Nika Salia & Oscar Zamora, 2020. "The maximum Wiener index of maximal planar graphs," Journal of Combinatorial Optimization, Springer, vol. 40(4), pages 1121-1135, November.
    Full references (including those not matched with items on IDEAS)

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